In scenes with a lot of shrubbery or tall grass, it's pretty much impossible to spot a sniper because he'll be behind the vegetation, not just nestled in it with camouflage that blends in well. The rifle scope can "burn through" the vegetation the same way you can see through nearby grass with binoculars. It's impossible to see through it if you're at a distance from the other side, unless he's silhouetted against a bright background.
They generally don't, at least in the U.S. military, because our adversaries of the last couple decades could rarely afford thermal optics. I have heard of using sleeping bags, though.